Question

Some children, playing on the beach, dig out sand for making a hollow cylinder in

the ground of radius 14cm and depth 20 cm. they then use this sand to make a

cone like structure of radius 14cm. what is the height of the cone?​

Answer 1

Answer:

20cm................

Answer 2

Given:

Some children, playing on the beach, dig out sand for making a hollow cylinder in the ground of radius 14cm and depth 20 cm. they then use this sand to make a cone like structure of radius 14cm.

To find:

Height of the cone.

Calculation:

When the children dug up the cylinder and used the same sand to create a cone , we can say that the volume of cylinder and cone is equal.

Volume of cylinder:

$\therefore \: V_{(cylinder)} = \pi {r}^{2} h$

$\implies\: V_{(cylinder)} = \pi {(14)}^{2} (20) \: \: \: \: .....(1)$

Now, volume of cone (considering height as 'l'):

$\therefore \: V_{(cone)} = \dfrac{1}{3} \pi {r}^{2} l$

$\implies \: V_{(cone)} = \dfrac{1}{3} \pi {(14)}^{2} l \: \: \: \: .....(2)$

Now , these volumes must be equal:

$\therefore \: \dfrac{1}{3} \pi {(14)}^{2} l = \pi {(14)}^{2} (20)$

$\implies \: \dfrac{1}{3} l = (20)$

$\implies \: l = 20 \times 3$

$\implies \: l = 60 \: cm$

So, height of cone is 60 cm.